Donald J. Trump finally told Republicans what they have long wanted to hear — that he would not run for president as an independent if he did not get the Republican nomination.

Apparently because he has said that before, and then appeared to back off the pledge, and the language appeared somewhat short of unequivocal. No matter: Republicans in the audience, and the person who asked him the question — Hugh Hewitt, the conservative radio host — burst into applause as Mr. Trump, looking uncommonly humble, gave his answer.

Mr. Hewitt asked the question noting that Republicans were worried that they would lose to Hillary Clinton if she got the Democratic nomination and Mr. Trump ran as an independent candidate. “I am totally committed to the Republican Party,” Mr. Trump said. “I am very honored to be the front-runner. I think I’ll do very well if I’m chosen.”

11:03 pm ETDec 15, 20152015-12-16T04:04:37+00:00

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Carly Fiorina during the debate on Tuesday night at the Venetian in Las Vegas.Credit Ruth Fremson/The New York Times

10:59 pm ETDec 15, 20152015-12-16T04:03:00+00:00

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Donald J. Trump and Gov. Chris Christie of New Jersey during a commercial break at the Venetian on Tuesday night in Las Vegas.Credit Ruth Fremson/The New York Times

It is not as if the Republican debate stage is not already crowded. Donald J. Trump, after looking bored for much of this debate, riled himself up to get into a fight with CNN, the host of this debate, and, in particular, one of the questioners, the conservative talk show host Hugh Hewitt.

Mr. Trump objected that, again and again, the CNN moderators at this debate, and at an earlier one involving second-tier candidates, were prefacing questions with, as he put it, “Mr. Trump said this,” or “Mr. Trump said that.” All of this led to the striking moment of Mr. Trump seeming to complain that he was getting too much publicity.

“I thought it was very unfair virtually the entire portion of the debate was Trump this, Trump that — in order to get ratings,” he said. “I think it’s very unprofessional.”

10:37 pm ETDec 15, 20152015-12-16T03:37:55+00:00

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Jeb Bush, Chris Christie and Senator Rand PaulCredit Ruth Fremson/The New York Times

Immigration has been a particularly contentious issue in the Republican primary, providing fodder for numerous attacks. Some of the candidates would pursue a path for undocumented immigrants to stay in the country legally, while others condemn granting what they consider amnesty. See more issues »

There were some important issues being discussed by Senators Rand Paul, Marco Rubio and Ted Cruz about national surveillance and immigration — in particular, the votes by Mr. Paul and Mr. Cruz in favor of legislation that cut back the ability of the government to collect telephone records — but they might have gotten lost in a deadening buzz of Washington speak.

And that provided a big opportunity for Gov. Chris Christie of New Jersey to jump in and remind people that in an era when anti-Washington sentiment runs high, he does not serve in Congress.

“This is the difference between having been a federal prosecutor instead of being one of 100 people debating it,” Mr. Christie said.

This is a big night for Jeb Bush and he seemed prepared early to grab his moment. When he was asked to back up his assertion that Donald J. Trump was unhinged for proposing a temporary ban on Muslims coming into the country, Mr. Bush took the opportunity to criticize Mr. Trump.

“Donald is great at the one-liners,” Mr. Bush said, before unleashing what sounded like a Trump one-liner. “But he’s a chaos candidate, and he’d be a chaos president.”

What was perhaps more striking about the exchange was how understated Mr. Trump was in his response: The words were there, but it is clear that Mr. Trump is not looking at Mr. Bush as much of an obstacle to his winning the Republican presidential nomination.

“Jeb doesn’t really believe I’m unhinged,” Mr. Trump said. “He said that very simply because he has failed in this campaign. He has been a total disaster.”

After the terrorist attacks in Paris in November, the presidential field split largely along party lines over whether to allow Syrian refugees into the United States. Most of the Republicans opposed admitting them, though two candidates expressed support for allowing Christian refugees. See more issues »

Donald Trump is the know-nothing candidate of the 21st century and cannot be our nominee.

— George E. Pataki

7:06 pm ETDec 15, 20152015-12-16T00:10:04+00:00

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George E. Pataki, Mike Huckabee, Rick Santorum and Senator Lindsey Graham at the Republican presidential debate hosted by CNN at the Venetian Tuesday in Las Vegas.Credit Ruth Fremson/The New York Times

Before the start of the so-called undercard debate on Tuesday night.Credit Ruth Fremson/The New York Times

The so-called undercard debates have been billed as J.V. affairs, an overflow room for low-polling candidates who are trying to get out of political purgatory.

On Tuesday night, four Republican presidential hopefuls will get another chance to make the case that voters should give their campaigns one last look. Senator Lindsey Graham, former Gov. George E. Pataki of New York, former Gov. Mike Huckabee of Arkansas and former Senator Rick Santorum of Pennsylvania have all struggled to gain traction in the polls and are all facing the prospect that this debate could be their last.

Mr. Huckabee saw a top staff member depart this week, Mr. Santorum and Mr. Pataki have remained unknown to most voters, and Mr. Graham is banking his candidacy on a surprisingly strong showing in New Hampshire.

The “happy hour” debate has been a launching pad for some candidates, such as Carly Fiorina, and Gov. Chris Christie of New Jersey managed to make it back to the main stage after slipping to the “appetizer” event last time around.

But with the Iowa caucuses just around the corner, the pressure is on for Tuesday night’s crop of early debaters to find a way to shine.